We have, by Theorem REF , that \(\operatorname{Ext}^n_R(M\otimes _RM^*,R)=0\) . Then, in view of Proposition REF , it follows that:
\(\operatorname{Ext}^n_R(M,M)=0.\qquad \mathrm {(\ref {ri}.1)}\) 
(i) This follows from (REF .1) and [1]}.
(ii) This follows from (REF .1) and Lemma REF .
(iii) This follows from (REF .1) and [2]}.
